WJD Open Notebook

I started a GitHub repository called UniversalAlgebra/Conferences in an effort to keep up with the vast number of meetings in these areas and help make summer travel plans accordingly.

The UniversalAlgebra/Conferences repository is simply a list of links to the conferences listed.

This post details the steps I use to update or install the latest version of the Java Development Kit (JDK) on my Linux systems.

Suppose the lattice shown below is a congruence lattice of an algebra.

Conjecture: If the three $\alpha_i$'s pairwise permute, then all pairs in the lattice permute.

It is not hard to see that 3-SAT reduces to the problem of deciding whether all coatoms in a certain partition lattice are contained in the union of a collection of certain principal filters. Therefore, the latter problem, which we will call the covered coatoms problem (CCP), is NP-complete. In this post we simply define CCP. Later we check that 3-SAT reduces to CCP, and then develop some ideas about constructing a feasible algorithm to solve CCP.

The questions below appeared on an online test administered by Jane Street Capital Management to assess whether a person is worthy of a phone interview.